GA Flight Instructor with student reported an NMAC in the traffic pattern at a non-towered airport with an aircraft that entered the pattern incorrectly and opposite direction of traffic. Both pilots took evasive action to avoid a collision.

Narrative

My student owns Aircraft X. We did 3 laps of touch and goes in ZZZ airport. There was only 1 other plane in the pattern Aircraft Y doing touch and gos - also with a cfi. On our third touch and go we made appropriate radio calls and turned crosswind then downwind. On downwind my student and I saw converging downwind traffic at the same time. I froze up. My student immediately banked hard left avoiding the collision. The cfi in the other plane said on the craft dude there's people in the pattern. Only then did the other plane talk on the radio-Aircraft X- he said I'm doing a 360 for spacing. When we got on the ground the other instructed in Aircraft Y said him and his student were on upwind when they say us nearly collide at 200 ft. I believed it to be 50 to 100 horizontal ft because I could see the pilot face in the cockpit. When the pilot of Aircraft X lands my student I go up to his plane. He gets out and the lineman confronts him about not talking on the radio and entering the pattern not on a mid 45 degree entry; he stated he's a cfi and looked embarrassed. I said; hey sir can we talk about the incident; the pilot just walked away and literally walked to another plane; and took off; not even preflighting it. Me and my student were shaken; we stayed in the lobby rehashing the ordeal for hours. When he lands the other aircraft a few hours later; I again try to approach the pilot of Aircraft Z and now he and claim it's a radio problem then walks off. The pilot never even said sorry for causing a near death experience. He then jumps back into Aircraft X and starts up and flies away. Again not even preflighting. My student have been grieving for the past day. He is scared for his life. The pilot is a danger to the community.